All Questions
Tagged with spin-models lattice-model
30
questions
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Breaking a classical ground state degeneracy by a quantum term and order-by-disorder
Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
- 28.4k
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Lattice symmetry operations in strongly spin-orbit coupled systems
I think this is a FAQ when we are studying the rotation operations of lattice spin systems, but I can't find much references.
Background
Considering a Hamiltonian defined on a triangular lattice:
\...
6
votes
2
answers
511
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Is there Difference Between 1D and 2D in Spin model?
The Motivation is That:In the Tensor Network method, they say 'time evolution MPS(Matrix Product State) work quite well in 1 Dimension'.
but as I think any 2D could be expressed by 1D
for example in ...
- 8,094
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Current Operators on Lattice
Peierls substitution method by taking the functional derivative of Hamiltonian can be used to determine the form of current-operator in continuum model (See Bruus-Flensberg) as well as lattice model. ...
- 126k
2
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2
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How to understand a Hamiltonian of the form $c^\dagger \sigma^x c$?
In a 2-dimensional lattice Dirac model (a discretized Hamiltonian on a lattice, the model could be found in this dissertation, equation (2.19)), I found a Hamiltonian with terms like:
$$ H = \sum_{m,n}...
- 60.3k
1
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77
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Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?
Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms:
$$
H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i
$$
The first is a collection of ...
- 29
1
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59
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Holley and FKG Lattice Conditions
There's an interesting exercise (page 13, Exercise 11) in Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice, which states that the following 2 statements are ...
- 207k
6
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1
answer
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Bogoliubov-de-Gennes (BdG) formalism of Hamiltonians
The Bogoliubov-de-Gennes (BdG) formalism of a Hamiltonian reduces the dimension of the Hilbert space we work on. For example, in 1D superconducting Hamiltonians with $N$ lattice sites, the actual ...
- 207k
2
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0
answers
61
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(In)finite lattice in quantum statistical mechanics: validity of phase classifications and TQFT [closed]
I would like to understand the motivation for studying quantum statistical mechanics, such as spin models, on an infinite lattice, or in other word, in the operator algebraic framework. I learned that ...
- 2,646
1
vote
1
answer
48
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Energy current in a quantum chain
I have seen in (e.g. this paper) the definition of the energy current in a chain with $H = \sum_{j=1}^L h_j$
where $H_j$ has support on the $k$ sites $j,j+1,j+2,...,j+(k-1)$ as
$$J_j - J_{j+1} = i[H, ...
- 2,292
6
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3
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Why can we choose spin-1/2 degrees of freedom to commute?
Edit 2:
The previous title of this question was "Why are qubits bosonic?" Thanks to the answers that have been provided so far, I now realize I asked my question in a sloppy way. The ...
- 207k
3
votes
2
answers
233
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Lattice gauge and spin network
I see the similarity between the Lattice Gauge and Spin Network.
(For example, both theories depict the node part as quantum (the latter is explained as spin).)
Are there any other mathematical, ...
- 1,540
2
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0
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123
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Spin glass observables in Monte Carlo simulations
I am currently simulating an Edwards-Anderson spin glass using standard Metropolis Monte Carlo techniques. The spins are placed on a 3D cubic lattice with periodic boundaries and take on Ising values (...
- 21
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2
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2k
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Kagome Lattice: Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
- 499
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1
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Is spin-1 Ising model exactly solvable (one dimension and two dimension)?
I am working on spin-1 Ising model and I am new in this field. it seems that spin-1 Ising model in one dimension can be exactly solved by transfer matrix similar with spin 1/2 Ising model, am I right ...
- 20.8k